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Countable and Full Exchange Rings

Pace P. Nielsen
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Abstract

We show that a suitable ring with a ``nice'' topology, in which convergent limits of units are units, is an \aleph_0-exchange ring. We generalize the argument to show that a semi-regular ring, R, with a ``nice'' topology, is a full exchange ring. Putting these results in the language of modules, we show that a cohopfian module with finite exchange has countable exchange. Also, all modules with Dedekind-finite, semi-regular endomorphism rings are full exchange modules.

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Pace P. Nielsen. 2004-08-25. Countable and Full Exchange Rings. https://doi.org/10.1080/00927870600936815

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